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Restrictions on symplectic fibrations

Jaroslaw Kedra
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Abstract

Moduli spaces of stable pseudoholomorphic curves can be defined parametrically, i.e. over total spaces of symplectic fibrations. This imposes several restrictions on the spectral sequence of a symplectic fibration. We prove that, under certain assumptions, a Hamiltonian fibration c-splits, i.e. the spectral sequence associated to the fibration collapses at E_2. Moreover, we obtain a new estimate of the rank of flux groups. In the appendix, we provide examples of nonzero Gromov-Witten invariants for blow-ups. As an application, we prove that any Hamiltonian fibration with fibre being projective space CP^5 blown-up along 4-dimensional symplectic submanifold c-splits.

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Jaroslaw Kedra. 2002-03-22. Restrictions on symplectic fibrations. https://arxiv.org/abs/math/0203232

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